Answers to Questions and Problems in the Text

Answers to Questions and Problems in the Text *Jim Dearden s audio presentations are available online, at www.aw-bc.com/perloff Ch8 1.The shutdown rule states that a firm should shut down when it can avoid additional losses by doing so. This occurs when losses would exceed fixed costs. If the firm can cover any portion of fixed costs by continuing production, it should do so. 2. Solution in text. 3. Solution in text. 4. As shown in Figure 8.2, before low-carb food became popular, the demand curve was D 1, it is not profitable to enter the market since the fixed cost is so high such that short-run average cost is about the market price. If the demand curve shifts rightward to D 2 due to the popularity of low-carb food, the firms make a positive profit in the short run. However, once the low-carb food fell out of the fashion, the demand curve shifts leftward and the firms exited the market. Figure 8.2 5. As shown in Figure 8.3, when demand increase from D 1 to D 2, the price increases as well. If the increase in demand is expected to be temporary, firms will produce Q 1. On the other hand, if the higher demand is expected to be permanent, firms will produce Q 2. In the long run, the market supply curve will be a horizontal line. 1

Figure 8.3 6. a. Assuming that the average cost and marginal cost all have U-shape, a firm s marginal and average costs are likely to rise with extra business. b. As shown in Figure 8.4, since the increased demand is only seasonal, it will not affect firms long run supply curve and the number of firms in the market if there is considerable entry cost. During peaked demand period, firms will operate to the right of the minimum of the short run average cost curve. Figure 8.4 2

7. With a competitive market, firms with higher average cost will be driven out of the market by lower-cost firm firms. The equilibrium profit will be zero. See Figure 8.5, the higher-cost firm with average cost curve AC 1 will be driven out of the market if there exists also lower-cost firm with average cost curve AC 2. Figure 8.5 8. See Figure 8.6, with a relatively high price for Grade A milk, the firms can produce a large amount of Grade A milk with a lower average cost if they adopt the new technology. Hence the high price of Grade A milk gives the incentive to adopt the technology for its production. Figure 8.6 9. Solution in text. 3

10. See Figure 8.7. The lower of average minimum variable cost will extend firm s supply curve downward. As a result, the market supply curve shifts rightward. Figure 8.7 11. a. Since Lesotho is a price taker in the world market, the demand curve it faces is a horizontal line. b. The increase in Chinese exports shifts its demand curve downward. c. The change in exchange rate makes its exports more expensive relatively, further shifts down its demand curve. d. See Figure 8.8, when the price falls below p 1, the firms will shut down temporarily. If the price falls below p 2, the firms will shut down permanently. Figure 8.8 12. Figure 8.9 shows the effects of China s entry into the generic art market. Without Chinese exports, the world supply curve starts with country A, whose cost is only higher than that of China. With large amount of Chinese exports, the world supply curve is dominated substantially by Chinese exports, as indicated by the first section of the supply curve. 4

Figure 8.9 13. As shown in Figure 8.10, due to the lower average cost, the long run average cost curve shifts downward and firms supply curves shift rightward. As a result, the horizontal market supply curve shifts downward. Figure 8.10 14. Solution provided in Jim Dearden s audio presentation. 15. Solution provided in Jim Dearden s audio presentation. 16. Solution provided in Jim Dearden s audio presentation. 17. One reason that firms increase the price of coffee only 14% may be that the demand of coffee is elastic. On the other hand, since the roast coffee producers do not have good substitute for raw coffee beans, they have to burden a large portion of the increase in raw coffee beans. 18. a. See Figure 8.11, the firm s supply curve shifts leftward due the storm. As a result, the market supply curse shifts rightward as well. b. If Tomato Fest suffered an economic loss in this case depends on the demand elasticity, which determines how the price responds to a lower supply. In this situation, an economic loss is defined as negative profit. 5

Figure 8.11 19. As shown in Figure 8.12, the profit first increases with the days of vacations and then decreases with it. The profit is maximized if D * days of vacations are taken. Figure 8.12 20. If the world demand curve crosses the supply curve in the flat section of the Brazil supply, there will be a unique equilibrium price and likely multiple equilibrium quantities along that section. Similarly, if the world demand curve crosses the supply curve in the following vertical section, there will be a unique equilibrium and likely multiple equilibrium prices. In either case, farmers in the United States will not produce cotton. 21. The logic behind the first claim is that the firm chooses not to charge the full price of one of the input, the rent. The logic for the second claim is that since it is charged a lower price for one of the input, the output price is also lower. 22. In either case, marginal cost is unaffected. The only difference is the magnitude of the upward shift in average cost. If the tax is collected every year instead of only once, but the total amounts are equal, the average cost curve is shifted up by more due to the increase in the tax. Long-run supply is also shifted upward due to the increase in the minimum point of the average cost. 23. In the short run, since there is no change in marginal cost, there will be no change in the equilibrium output level or price. Profits will be reduced by the amount of the tax. The only exception is if the firms were close enough to the shutdown point such that the payment of the tax increases losses beyond fixed costs (assuming payment of the tax is not required if the firm shuts down). In this case, with identical firms, equilibrium quantity drops to zero. 6

24. Such a tax will not affect the marginal cost. However the tax incidence will be shared by the groceries and the consumers. The amount of tax passed on to consumers will be determined by the demand elasticity of grocery bags. 25. Solution in text. 26. See Figure 8.13. In this case the firm is producing more than the long-run profit maximizing output level of 110. Profits are currently equal to area abcd, but would be increased to area ebfg with the optimal plant size. Figure 8.13 27. No. Although horizontal factor supply curves would generate a horizontal firm supply curve, it could also be that one input increases in cost at the same rate and that another decrease in cost. In either case, as firm and industry output expands, average cost will remain unchanged and the industry long-run supply curve will be horizontal. 28. If Arizona starts collecting a specific tax (a) on its firms, then they may be driven from the market. Assuming that firms in California and Arizona have initial costs to start, a specific tax on Arizona oranges could have two possible effects. If there is unlimited entry by California firms, the long-run supply curve will be unaffected, and all Arizona firms will be driven from the market due to their cost disadvantage. If entry in California is limited, then the long-run supply curve becomes a step function, as shown in Figure 8.14. All output up to Q C would be supplied by California firms, after which costs (and so the supply curve) shift upward by the amount of the tax for output supplied by Arizona firms. Figure 8.14 7

29. See Figure 8.15. In the graph on the right, a decrease in the demand for real trees caused by the increase in artificial tree sales shifts the demand curve to the left. The supply curve shifts to the left due to the decreased number of tree growers. The result is an increase in price to $26.50, and a decrease in quantity to 33 million. On the left, each retail tree seller purchases trees at an average cost of $20, and sells for the market price of $26.50. Figure 8.15 30. When the bribes lose their tax-deductible status, the cost of making a bribe increases. The supply curve shifts to the left, just as it would if a tax were enacted (similar to Figure 8.10). The increase in the price of bribes reduces the equilibrium quantity. In the product market, if we view the bribes as part of the cost of doing business, an increase in the cost of bribing foreign officials would shift the marginal cost curve upward in the product markets, reducing the supply. 31. If importers were allowed to bring gas to California at a 15 cent surcharge, it would not alter the normal equilibrium, as shown as p *, G * in Figure 8.16. However, in the event of a large leftward shift of the supply curve, it would prevent prices from rising above p * 0.15. In the graph, the horizontal portion of the supply curve represents imported gas at the surcharge price. As a result of these imports, prices rise only to p * 0.15 and quantity is G 1, instead of a price increase to p and a drop to the no import level G NI. Figure 8.16 8

32. Marginal cost is computed by taking the derivative dc/dq. Profits are maximized by setting MC MR p. For the function given, MC 10 2q q 2. Thus profits are maximized when p 10 2q q 2. The supply curve is p 10 2q q 2 for P 9.25. 33. Solution in text. 34. In the long run price equals marginal cost, and profits are zero. Thus given that industry output Q nq, the following will be true in long-run equilibrium, p 24 nq. Therefore, 24 nq 2q (24 nq)q 16 q 2. Solving these equations for q, n, Q, and p yields q 4 n 4 Q 16 p 8. 35. Solution in text. 36. Solution in text. 37. Solution in text. 38. Solution in text. 39. After tax profit is (1 ) pqc( q) and the profit maximizing output after the tax is imposed is: ( q) C( ) (1 ) p 0 q q q 1 or p MC( q)(1 ) 0 the first order condition. Differentiating this with respect to the ad valorem tax rate yields: MC q 1 2 (1 ) MC( q)(1 ) 0 q and rearranging: q MC( q) 0 MC (1 ) q 40. Solution provided in Jim Dearden s audio presentation. 41. Solution provided in Jim Dearden s audio presentation. Ch9 1. See Figure 9.5. As demand becomes more elastic, the welfare effect of specific tax becomes larger because there is a larger change in the equilibrium quantity. In the graph, D 0 is more elastic than D 1 at point a. When a specific tax shifts the supply curve upwards, the welfare loss with the more elastic demand curve is abc. With D 1, the welfare loss is only adf. 9

Figure 9.5 2. See Figure 9.6. The price ceiling (p c ) on gasoline reduces welfare by the areas abd bcd. The new consumer surplus is area gacf, and producer surplus falls to area fch. Figure 9.6 3. See Figure 9.7. An individual receiving a gift valued at G increases his or her utility from U 0 to U 1 (at point b). The same individual receiving cash in an amount equal to the cost of G increases his or her utility to U 2 (at point c). The reason for the lower utility in the case of the gift is that it limits the individual s ability to substitute between the gift good and other commodities (i.e., in the figure, the individual cannot reach point c, where the marginal rate of substitution equals the price ratio). 10

Figure 9.7 4. Solution in text. 5. See Figure 9.8. The welfare loss from the tax is equal to area abc. If the ad valorem tax is levied on firms, then the supply curve will shift leftward. Also note that it is not a parallel shift as the price goes up, the original supply curve and the new supply curve will get farther apart creating a cone shape (narrower near the origin of the graph and wider as you move farther away from the origin). Figure 9.8 6. See Figure 9.9. The welfare loss due to the minimum wage is area abc. When the minimum is instituted, employment falls to L 1 from L 0. Because labor supply at the new higher wage increases to L 2, unemployment is increased by the institution of the minimum. Because of the excess supply, less experienced workers are likely to be losers with the new policy. In addition, if discrimination exists on the basis of age, gender, or race, those workers in the less desired group are also likely to be hurt by the minimum wage. 11

Figure 9.9 7. Solution in text. 8. Owners of existing billboards would not oppose the ban because it creates an entry barrier and so also market power for existing sellers. Producers would then be able to set prices above marginal cost, and transfer some of the consumer surplus to producers. Exclusive of external effects, welfare will fall, as a deadweight loss is created. The consumers are the purchasers of billboard space. The producers are billboard owners. Welfare is improved if the increase in billboards was creating a negative externality by making the scenery less enjoyable. 9. See Figure 9.10. With the price increase, producers gain A, but lose D. The payment x must be enough to compensate producers for their net loss from the price increase (x D A). With this payment, producer welfare is unchanged, but consumer welfare falls by A B. With a price support program, consumer surplus would be the same as with the lump sum payment program, but producer surplus would be A B C D E F. A quota set at Q 1 producer surplus is A B C D E. With the quota set at Q 2 producer surplus is A C. Figure 9.10 12

10. See Figure 9.11. At the original price, P 0, consumer surplus is A B C, and producer surplus is E F. If officials want to reduce the number of visits to Q *, they can either increase the price to P 1, which reduces consumer surplus by B C, or they can institute a quota and leave the price unchanged. With the quota, consumers retain area A B, and area C is deadweight loss. Area F is eliminated under either scenario. Assuming the park is charging marginal cost for admission, which is constant, there are no welfare effects from the change in area F. Figure 9.11 11. See Figures 9.12a and b. In the sugar market, the quota increases price, reduces output, and causes a deadweight loss of A. In the corn sweetener market, demand is increased due to the increased cost of the substitute, raising prices from p 1 to p 2. Figure 9.12 13

12. See Figure 9.13. The government prefers the tariff. In either case, consumer surplus is reduced to area A. With the quota, the government collects no revenue. With the tariff, the government collects B C D E as revenue. Figure 9.13 13. See Figure 9.14. The subsidy increases consumer welfare by B C, but costs the government B C D. The net change in welfare is D. Figure 9.14 14

14. If we assume that the Canadian supply curve is perfectly elastic (horizontal) at the open-market price, there would be no welfare effects in Canada. Figure 9.15 shows the effects on the U.S. markets. If the open market supply curve (U.S. plus Canadian) is S 0, and the U.S. only supply curve is S US, then the effect of the import restriction is to increase the price to U.S. water users from p to p. Consumer surplus falls from A B C D to D only. U.S. producers gain A, but B C represent deadweight loss. Figure 9.15 15. With the subsidy consumers benefit, but taxpayers (including those same consumers) bear the burden of the subsidy, and a deadweight loss results, as the number of apartments rented exceeds the unregulated quantity. The price ceiling is analogous to the figure shown in Solved Problem 9.3. In this case consumers who are still able to find an apartment gain, but fewer apartments are available. With the price ceiling, the good is underprovided, which again leads to a deadweight loss, although in this case there is no tax burden as there is no government expenditure. The supply and demand elasticities are important determinants of the size of the deadweight loss, as in both cases, the loss is created by the wedge between supply and demand at the new quantity. The relative slopes of the curves (which are directly related to the elasticities) determine the size of the wedge. 16. Solution provided in Jim Dearden s audio presentation. 17. Solution provided in Jim Dearden s audio presentation. 18. Solution provided in Jim Dearden s audio presentation. 19. Solution provided in Jim Dearden s audio presentation. 20. See Figure 9.16. The left panel shows the impacts of medallions or annual licenses. The long run supply curve changes from S 1 to S 2. The area C is the deadweight loss. With medallions, the producer surplus B goes to the medallion owner; while with annual licenses, the surplus goes to government. The right panel shows the case of daily tax. The area C is the deadweight loss and the area B is the tax revenue. 15

Figure 9.16 21. As shown in Figure 9.17, the ban of self-serve shifts the supply curve from S 1 to S 2. As a result, consumer surplus decreases by area (A B), the social deadweight loss is (B C), and gas stations get extra producer surplus equal to area (A C). Figure 9.17 22. As shown in Figure 9.18, the USDA recommendation shifts the demand curve from D 1 to D 2. As the result, the consumer surplus increases from area (A B) to area (B C). Figure 9.18 16

23. As shown in Figure 9.19, the government subsidy shifts the supply curve from S 1 to S 2. As a result, consumer surplus changes from (A B) to (A B C E), producer surplus changes from (C G) to (C G B D), and government expense changes from zero to (B C D E F). Figure 9.19 24. As shown in Figure 9.20, under subsidy, consumer surplus increases from A to (A B C), and produce surplus decreases from B D to D. If the government imposes a large tariff such that the domestic price is raised to the level without the subsidy, then the consumer and produce surpluses will return to the levels without the subsidy. Figure 9.20 25. As shown in Figure 9.21, the government subsidy to the cotton producers shifts the supply curve from S 1 to S 2, and the subsidy to the buyers further lowers the price from p 2 to p 3. As a result, consumer (buyer) surplus increases by (C D G H I) and producer surplus increases by (L H C). The government expense increases from zero to (C D E F G H I J). 17

Figure 9.21 26. As shown in Figure 9.22, the tax on wireless service creates deadweight loss equal to area (B E). On the other hand, assuming the tax would have no effect on the demand of landline serve, there will be no deadweight loss. The area (A B C) is the government tax revenue. Figure 9.22 27. See Figure 9.23. Consider an imported good first. With the embargo, the consumer surplus decreases by (B C), and producer surplus increases by B. On the other hand, for an exported good, the consumer surplus increases by (B C) and producer surplus decreases by B. Figure 9.23 18

28. As shown in Figure 9.24, the tariff will decrease consumer surplus by the area (A B), while the tariff revenue is equal to area (A C). If C B, the welfare in the importing country improves. Figure 9.24 29. Solution in text. 30. Solution in text. 31. CS 0.5(a/2)(a/2b) a 2 /8b. 32. Ap* *( 1) *( 1) 1/ Ap PS Ap ( Q/ A) dq. 0 1 33. The initial equilibrium is Q * 30, p * 30. The tax reduces output to 29. Consumers pay $31 and producers receive $29. Tax revenue is $58, and deadweight loss is $1. 34. Solution in text. 35. a. The equilibrium price and quantity without the tax is p 5 and Q 50. With the tax, the demand function will be Q 100 10(p 1) and the supply function remains the same. Hence the equilibrium will be p 5.5 and q 45. b. Consumer surplus decreases by (50 45) * 0.5/2 23.75, producer surplus decreases by the same amount. Government tax revenue is 45. Hence the deadweight loss is 23.75 * 2 45 2.5. 36. a. With the price ceiling, the equilibrium will be p 3 and Q 30. b. The consumer surplus increases by 2 * 30 2 * (50 30)/2 40, producer surplus decreases by 2 * (50 30)/2 80. So the social deadweight loss is 40. 37. Solution in text. 38. Solution provided in Jim Dearden s audio presentation. 39. Solution provided in Jim Dearden s audio presentation. Ch11 19

1. See Figure 11.6. Because there is no supply curve, if the demand curve shifts from D 0 to D 1, output increases from Q 0 to Q 1, but price remains unchanged. Figure 11.6 2. The effect of a franchise tax or lump sum tax on a monopoly is to reduce profits by the amount of the tax. Because there is no change in marginal cost, the profit-maximizing/loss-minimizing output and price remain unchanged, with one exception. If the tax is large enough, losses may exceed variable costs. If that is the case, the firm will shut down (produce no output) in order to minimize losses. 3. When the average total cost curve lies above the demand curve at all output levels, the monopolist cannot earn positive profits. 4. See Figure 11.7. The values of price and quantity depend on the demand curve drawn by the student. In the given graph, profit-maximizing quantity is 4 and profit-maximizing price is 8. Profits are area abcd and the deadweight loss is area bef. Figure 11.7 5. Solution in text. 20

6. No. In order for a firm to be a natural monopoly, its production must exhibit economies of scale, that is, firm s average cost curve must be downward sloping. If the firm operates in the upward sloping region of its average cost curve, it is possible that two or more firms could produce in the same industry more efficiently than one firm. 7. No. The utility is producing at the section of AC that is upward sloping, and therefore is not a natural monopoly. 8. See Figure 11.8. A competitive firm maximizes long-run profits by setting LMC p, as long as price exceeds average cost (it should shut down if p LAC). Because marginal cost is above average cost only where AC slopes up, the firm will never operate in an area where average cost is falling. A monopolist maximizes profit by setting MR MC, which can occur on either the upward- or downward-sloping portion of the LAC curve. In the graph, D M represents the demand curve faced by the monopolist, and d C represents the demand curve faced by a competitive firm. Figure 11.8 9. A monopolist may set price equal to marginal cost if other firms can enter costlessly. If there is free entry, any price above marginal cost will attract other firms. Thus even though the firm has no current competitors, it sets price equal to marginal cost to deter entry of potential competitors. Also, if not all customers are charged the same price (price discrimination), the firm may want to sell the last unit where price equals marginal cost (Chapter 12). 10. See Figure 11.9. If the government sets a price cap between the monopoly price and the socially optimal price, output increases from Q M to Q R, and deadweight loss is reduced from area abc to cdf. Figure 11.9 21

11. See Figure 11.10. To be on the contract curve (Pareto efficiency) requires that all goods be traded at competitive prices. Because Jane is a monopolist, she sets the price of wood above the competitive price. At this higher price, she receives more candy bars per unit of wood than with competitive prices, and consumers end up with less wood than with competitive prices. The monopoly price line in the graph depicts this higher price ratio. Instead of reaching the Pareto-optimal solution at a, Jane is able to use her market power to force the solution at b, which is off the contract curve and Pareto inferior. Figure 11.10 12. See Figure 11.11. In this case, MR curve coincides with the demand curve. Equilibrium quantity is 100 and equilibrium price is $100. Consumer surplus is zero and producer surplus is ($100 $10) 100 = $9000. If a price ceiling of $30 is imposed, consumer surplus increases and producer surplus decreases by area abcd. There is no deadweight loss. Figure 11.11 22

13. Wholesale price of milk represents the marginal cost for retailers, who sell to consumers. In Figure 11.12, suppose prices at the wholesale level fall 30.3% from $2.00 to $1.394 per gallon, or $0.606 per gallon. That is, for retailers, marginal cost shifts from MC to MC. If the original retail price were $3.00 per gallon, a 30.3% price decrease would mean the new price of $2.09, a drop of $0.91 per gallon. However, the negative slope of the demand curve results in a price decrease that is less than $0.91. The new retail price, for the given demand curve, is $2.50. In other words, price at the retail level may not fall by the same percentage as the wholesale level due to the slope of the demand curve. Figure 11.12 14. See Figure 11.13. Summing the demand curves horizontally yields the market demand curve. Once the price is set, quantity in each market is determined from the individual product demand curves. If the firm charged different prices in each market, physicians could simply prescribe the lower-priced version of the product. Figure 11.13 23

15. Once a book is online, it is available to consumers for free. As a result, the publisher may loose some consumers after the copyright expires. Limiting the length of a copyright (in the U.S. or elsewhere) would encourage the publisher to charge a higher price for the novel as the publisher attempts to recoup the cost of publishing the novel and earn profit in a shorter period before the copyright expires. After the copyright runs out, the publisher may lower the price of the novel to stay competitive with the online version. 16. This test is relevant because if the club were maximizing revenue, it would be operating at the level MR 0, where the elasticity is 1. 17. Consider a small hotel where the jammer would cost $25,000. If the expected profit from room phone service is $A per day per room and the number of rooms in the hotel is B. Then if $365AB $25,000, it is profitable to install a jammer. 18. See Figure 11.14. Assume that Bleyer Industries Inc. has a production process described by the marginal cost curve MC1. As a monopoly, Bleyer Industries Inc. can charge price P 1, while selling Q plastic Easter eggs. Since 1 P is above Bleyer s average total cost AC at the level of 1 Q1, Bleyer is profitable. The Chinese firms have lower production cost; we can denote their marginal cost as MC2. Once the Chinese firms start competing with Bleyer, they can charge a price as low as P. Such a 2 low price would force Bleyer to exit the market because P2 is below AC and Bleyer cannot make positive profit. Figure 11.14 19. a. Assume demand is D 1. Then, the consumer surplus is a d h; the producer surplus is b i; and social deadweight loss is c e. If the monopoly behaves like a price taker, the quantity will be Q c as shown in the figure. b. When the new demand curve, D is tangent to the original one at 2, (Q*, P * ), as shown in Figure 11.15, the price and quantity will not change. However, the quantity if the monopoly behaves like a price taker will change to Q 2. Consumer surplus will decrease and will be the area a h under the concave demand curve; producer surplus will remain as b i; deadweight loss will decrease to c. 24

c. Under the convex demand curve, D, 3 the price and quantity will be the same as in the linear case. But under the price-taker assumption, the quantity supplied will be Q 3. Consumer surplus will increase and will be the area a d h f; producer surplus will remain as b i; deadweight loss will increase to c e g. D 3 D 2 Figure 11.15 Q2 Q3 20. See Figure 11.16. After the remove of the tariff, the former monopoly will sell its products at the world price p w. The new quantity Q w is determined by the intersection of its MR curve and world price. The consumer benefits from the removal of tariff and the former monopoly suffers losses. Figure 11.16 21. When the hoi polloi buy the chocolate, the snobs won t buy. So the monopoly is facing a relatively flat demand curve, which suggests a low price, high quantity outcome. On the contrary, if the hoi polloi do not buy the chocolate, the snobs will buy. In this situation, the monopoly will face a steep demand curve, resulting in a high price, low quantity outcome. If the demand curve for the snobs is substantially steeper than that for the hoi polloi such that the profit from the former is larger than that from the latter, the monopoly will choose to cater to the snobs. 25

22. Solution in text. 23. Set MC MR and solve: MR 100 2Q MC 5 51002Q * Q 47.5 * p 52.5 If CQ ( ) 100 5 Q, the answer does not change because marginal cost is still MC 5, and therefore the profit-maximizing condition is still the same. 24. Set MC MR and solve. MR dr d d (10 Q Q) (10 Q dq dq dq ) 5Q MC 5 * Q 1 * p 10 1/2 1/2 1/2 25. The total profit is total revenue minus total cost and tax. TR ( TC tq) P( Q) Q ( C( Q) tq) The first-order condition is d d ( TR ( TC tq )) MR ( MC t ) 0 dq dq Imposing tax is equivalent to increasing the marginal cost, i.e. MC MC t. Hence after tax is imposed, output will drop, price will increase and profit will be smaller. 26. When the demand curve is linear, the marginal revenue curve will always be linear with twice the slope of the demand curve. This is true because when multiplying the demand curve by Q to obtain total revenue, we always obtain a squared term in the revenue function, which then doubles the slope when we take the derivative to obtain marginal revenue. For example, if the demand curve is P a bq TR aq bq 2 dtr MR a2bq dq Because the slope of MR is double of the slope of the linear demand curve, MR curve always crosses the MC segment in the middle between the y-axis and point ec (see figure in the Botox application). Hence triangles A and C have one equal side and three equal angles, which implies that these triangles are equal. 27. The inverse demand function is p 775 375Q. Imposing a specific tax of $75 will be equivalent to shifting the demand curve to p 700 375Q. With MC 25, profit-maximizing quantity and price are Q 0.9 and p 437.5. The new deadweight loss will be (437.5 25)(2 0.9)/2 $226.875 million. 26

28. With a price ceiling of $200, monopoly will produce Q (775 200)/375 1.53 million vials and the deadweight loss will be (200 25) * (2 1.53)/2 $41.1 million. 29. Solution provided in Jim Dearden s audio presentation. 30. Solution provided in Jim Dearden s audio presentation. 31. The price/marginal cost ratio is 99/45.37 2.18. Lerner Index is P MC/ P 99 45.37/99 0.542. Using the formula for the Lerner Index, the elasticity is.85. 32. Solution in text. 33. The Lerner Index is (1840.8 100)/1840.8 0.95. Hence Tenet believes that the elasticity it faces is 1.06. 34. The price/marginal cost ratio is 5000/2000 2.5. The Lerner Index is (5000 2000)/5000 0.6. Hence Segway believes it faces a demand elasticity of 1.67. 35. The price/marginal cost ratio is 499/258 1.93. The Lerner Index is (499 258)/499 0.48, and the elasticity Apple believes it faces is 2.08. 36. The Lerner Index is (84.95 37)/84.95 0.56. Hence Stamps.com believes that it faces a demand elasticity of 1.79. 37. Solution in text. 38. In the competitive case, equilibrium is found by equating supply and demand curves, D S: 1.787 0.0004641Q0.496 0.00020165Q Then Q P * C * C 3429.2151 lb 0.19550 $/lb Once the specific tax $0.01 is imposed, the supply curve, which is also MC, shifts up (see Figure 11.17a). To find the after-tax equilibrium, we solve D S S 1.787 0.0004641Q0.496 0.00020165Q0.01 Q C 3414.1945 lb P 0.20247 $/lb This suggests that tax incidence in the case of competition is C * p P C PC 0.20247 0.19550 0.7 70% 0.01 In the monopoly case, pretax profit-maximizing output and price levels are found by equating MC and MR (see Figure 11.17b). Marginal revenue is dr d d MR ( PQQ ( ) ) ((1.787 0.0004641 QQ ) ) dq dq dq 1.787 0.0009282Q 27

Marginal cost is the same as in the competitive case. Then, MR MC means that 1.787 0.0009282Q0.496 0.00020165Q Q P * M * M 2020.71 lb 1.787 0.00046412020.71 0.8492 $/lb After specific tax is imposed, MC shifts to MC and monopoly chooses output that satisfies the following condition Then MR MC MC 1.787 0.0009282Q0.496 0.00020165Q0.01 Q M 2011.7714 lb Q 1.787 0.00046412011.7714 0.8533 $/lb M Tax incidence on consumers in the case of monopoly is * p P M PM 0.8533 0.8492 0.41 41% 0.01 Figure 11.17 28

39. Consider constant marginal cost and suppose the monopoly is facing a linear demand function with inverse demand function p a bq. The monopoly will produce Q (MC a)/2b, where MC is the lower of two marginal cost at the factory with lower MC, and zero unit at the factor with higher MC. Suppose both factories have increasing marginal cost, the monopoly will produce at two factories Q 1 and Q 2 such that MC(Q 1 ) MC(Q 2 ) MC. 40. a. If the consumer cannot steal music, the total demand function function will be p 120 Q/2. The monopoly will set MR 120 Q 20, such that Q 100 and p 70. Consumer surplus will be 2500, profit and producer surplus will be 5000, and deadweight loss will be 2500. b. If the dishonest customer can steal music, then the total demand function will be p 120 Q. The monopoly will set MR 120 2Q 20, such that Q 50 and p 70. c. When dishonest customers can pirate the music, consumer surplus will consist of consumer surplus of honest and dishonest customers. Consumer surplus of dishonest customers will be 7200 and consumer surplus of honest customers will be 1250; therefore, total consumer surplus will be 7200 1250 8450. Producer will receive profit and surplus only by selling to the honest customers. Profit and producer surplus will be 2500. Deadweight loss will be 1250. 41. Solution in text. 42. a. To solve for the expansion path, set the ratio of the marginal products equal to the ratio of the input prices (see Appendix 7C) MPL MP r This gives the equation for the expansion path K L 0.25L. See Figure 11.18. r b. Substituting the expansion path into the production function yields L 2Q, and K 0.5Q. Thus C(Q) wl rk w2q r 0.5Q 1(2)Q 4(0.5)Q 4Q. c. Long-run profit-maximizing output is where LMC MR. dc LMC 4 dq dr d d 2 MR ( P( Q) Q) (100 QQ ) 100 2Q dq dq dq K Q * 48 p * 52 29

d. To solve, plug the capital labor ratio K 0.25L and the output level (48) into the production function. See Figure 11.18. L K L L L 1/2 1/2 1/2 1/2 48 (0.25 ) 0.5 L * 96 K * 0.25 96 24 Figure 11.18 43. Solution provided in Jim Dearden s audio presentation. 44. Solution provided in Jim Dearden s audio presentation. Ch12 1. In order to price discriminate, Alex must have market power the ability to set prices. Consumers must have varying price sensitivities, and Alex must be able to identify individual consumers or groups of individuals based on willingness to pay. Alex must also be able to prevent reselling after the initial sale. 2. Solution in text. 3. Solution in text. 4. The pharmaceutical firms offer the discount to low-income seniors because the seniors would probably not purchase the medicines if they were not discounted. By segregating this portion of the market, they are able to price discriminate profitably because the marginal cost of producing the extra medications is very low. Thus if they can still charge higher prices to the rest of the market, they will profit from the discounted prescriptions as well. (In addition to the short-run profits, the pharmaceutical firms get good publicity, which could forestall more costly regulation in the future.) 5. Since adults cannot use children s tickets to enter Disneyland, there won t be a resale problem. On the other hand, for nonlocal visitors, a small difference in ticket price does not mean much compared to their travel cost. In other words, their willingness to pay for the price is higher than locals. 30

6. When there is a big price different across the border and shipping the car from Canada to the United States is relatively cheap, consumers in Canada are able to make a profit by reselling their cars in the United States. To prevent this kind of resale that would decrease Ford s profit from price discrimination, Ford required Canadian dealer to sign an agreement that prohibited moving vehicles to the United States. Since the prevention might not be effective, in the following year, Ford cut the supply in Canada to only 2000 cars to practically eliminate the resale problem. 7. If Amazon can effectively monitor individual customer s shopping pattern and history and offer a different price accordingly, this is essentially first-degree price discrimination. 8. If the difference in the cost of a car renting service is equal to the difference in the rental price between the two cities, then there is no price discrimination. Otherwise, there may be price discrimination, especially as resales of the service is practically impossible. 9. Lower profit margin indicates the PC market is becoming more competitive. In other words, the market power of PC producers is decreasing, therefore lowering their ability to price discriminate. 10. a. This is third degree price discrimination. Suppose 1000 tickets were available, then price is determined by the bidder with the 1000th highest willingness-to-pay. All bidders with higher willingness-to-pay get the same price. b. This is first degree price discrimination as each bidder is charged at a price equal to his or her willingness-to-pay. 11. The difference in profit between a single price monopoly and perfect price discrimination is the area A and C in the application, which is $375 million. 12. The union can set the price at the level w * where demand and supply curves cross and request a lump-sum contribution whose total is equal to the area below the demand curve and above the price level w *. If the workers are not identical, say, if their ages are different, then the value of that uniform lump sum contribution may be different for different workers. 13. See Figure 12.3. The monopolist produces where price equals marginal cost. Total revenue is the area under the demand curve from the origin to Q *, or OafQ *. Total cost is 0dbQ *. Profits are adg gbf. Figure 12.3 14. Yes. Even if a consumer purchased 40 units per day, the average price would just equal the monopoly price, but the consumer surplus would fall from $450 to $400. In addition, the consumer in panel (b) pays $60 for 30 units, but the consumer in panel (a) must purchase 40 units to achieve the same average price. If they only bought 30 units, their average price would be $63.33. 15. See Figure 12.4. Output expands, as do profit and consumer surplus. When the markets are combined, * the monopolist sells Q 2 for $5, all to customers in Market 2. When the markets can be separated, 31

* price and quantity remain unchanged in Market 2, but the monopolist also sells Q 1 for p 1. Figure 12.4 16. Before the item is discounted, the department store attempts to sell the item to customers with relatively high reservation prices. If after a while the item is not sold out, the department store may try to sell the item to customers with lower reservation prices by putting the item on sale. 17. Yes. The monopoly s ability to price discriminate depends on the marginal cost. Suppose there are two groups of potential consumers. If the marginal cost is so high that one group will not buy the good at a price acceptable to the monopoly, then the monopoly is not able to price discriminate in this case. 18. No. If no consumers want the second product, profits are reduced by bundling it with the first product. The reason is that, because there is no demand for the second product, consumer demand for the bundled products will be equal to the demand for the first (desired) product alone. If there is no secondary market for the undesired product and the consumer must pay to dispose of it, then profits will be reduced rather than increased, as consumer demand falls to reflect the disposal cost. 19. If m 7, the marginal revenue curve crosses the marginal cost curve above the kink point. The monopoly will charge the monopoly price as if there is only one country, the country with higher demand. If m 4, the marginal cost curve crosses the marginal revenue curve three times, including the vertical portion of the marginal revenue cost. At the first cross point to the left of the kink point, we have 9 2Q 4. Hence Q 2.5 and p 6.5, the profit is 2.5 * (6.5 4) 5.25. For the cross point on the vertical section, Q 3 and p 6, the profit is 3 * (6 4) 6. For the cross point to the right of the kink point, 4 7 (2/3)Q. Hence Q 4.5 and p 5.5. The profit is 4.5 * (5.5 4) 6.75. Hence the monopoly will set the price at 5.5. 20. Abbott raised the price of Norvir such that it can make more profit from it if the demand elasticity is low. At the same time, not raising the price of Kaletra will give its own product a price advantage on the market. 21. Solution provided in Jim Dearden s audio presentation. 22. Solution provided in Jim Dearden s audio presentation. 23. Solution provided in Jim Dearden s audio presentation. 24. Solution provided in Jim Dearden s audio presentation. 25. a. The marginal cost is zero, so the MC curve is the X axis. The amount of tickets sold will be T *, 32

where the MR curve intersects X axis. b. The concerts failure may indicate monopoly price, but not that the monopoly set too high a price. c. If the monopoly can perfectly price discriminate, it can obtain all the producer surplus below the demand curve. 26. No, it is not reasonable to conclude that U.S. drivers subsidize European gasoline prices. If oil companies have market power in the United States and Europe and can price discriminate, they will treat each market as a separate market setting prices and quantities at profit-maximizing levels independent of the other market. 27. One possible explanation for higher magazine prices at a newsstand, rather than through a subscription, is the higher transaction cost of selling magazines through a network of newsstands. Besides the transaction cost, the desire to increase magazine sales that influences publisher s ability to attract advertising revenue is another strong motivator to lower the price of a subscription. 28. Solution in text. 29. Solution in text. 30. Solution in text. 31. The price charged in Canada is $15 * (1 33%) 20. Using Formula (12.2), we can get the elasticity of Canadian consumer is 1.05. The price charged in Japan is $25, hence the elasticity is 25/24 1.04. 32. Solution in text. 33. Setting marginal revenue equal to marginal cost yields Q * 30, p * 60. Profit is $900, consumer surplus is $450, welfare is $1350 (PS CS), and deadweight loss is $450. 34. The profit function of the monopoly described in Figure 12.3 is p Q p Q Q p Q Q mq 1 1 2 2 1 3 3 2 3 The monopoly faces a demand curve p 90 Q. Then, Q 90 p and we can write Q1 90 p1 Q2 90 p2 Q 90 p 3 3 Using these expressions, the profit function can be rewritten as p190 p1 p290 p2 90 p1 p390 p3 90 p2m90 p 3 p190 p1 p2p1 p2 p3p2 p3m90 p3 2 2 2 90p p p p p p p p 90mmp FOC: 1 1 1 2 2 2 3 3 3 33

90 2 p1 p2 0 p 1 p1 2p2 p3 0 p 2 p2 2p3 m0 p 3 Here m 30. and p3 45. Solving simultaneously, we find that profit-maximizing prices are p1 75, p 2 60, 35. a. The monopoly can set the price to be 60 and the minimum amount to be 60 such that to achieve the same outcome as in perfect price discrimination case. b. For a initial price of 90, the total demand will be zero. 36. Using Equation 12.2, p US (1 1/2) 10 p J (1 1/5) p US $20, p J $12.50. 37. Set marginal revenue in each market equal to marginal cost to determine the quantities. Plug the quantities into the demand functions to determine prices. MR 1 100 2Q 1 30 MC MR 2 120 4Q 2 30 MC Q 1 35; p 1 65 Q 2 22.5; p 2 75 38. Marginal revenue depends on price and elasticity of demand: 1 1 MR p1 1 1 MR 2 1 p2 1 2 From Solved Problem 12.3 we know that p1 p2 60. Since multimarket price discrimination leads 1 2 to prices that equate marginal revenues, that is, MR MR, we may write 1 1 p11 p21 1 2 1 1 601 601 1 2 39. Suppose a two-part tariff includes a fixed entry fee F, plus a per-unit cost m. In this case, the average price per unit is F/q m, which exceeds the marginal price m. Thus consumers who purchase more units pay a lower average or per-unit price. 1 2 34

40. See figure in Solved Problem 12.4. Without advertising, the optimal number of subscriptions is 1 determined by the intercept of MR and MC. This gives optimal output and price levels Q1 and p. 1 Presence of advertising has the same effect on the demand curve as a subsidy, that is, demand shifts 1 2 2 outward, from D to D. The new optimal point is set by the intercept of MR and MC. With advertising, the new equilibrium is a pair Q2 and p. Increasing 2 a increases subscriptions 41. Giving a lump-sum subsidy to Canadian publishers lowers their marginal cost regardless of how many subscriptions they sell. If MC drops, the publisher can charge a lower price for a subscription, which will increase subscription sales. 42. Assume one unit of advertising costs $1. Then monopoly solves max R( pa, ) Cp ( ) A pa, First order conditions are R dc 0 p p dp R 10 A A * A pair p and A * that solves the first order conditions maximizes monopoly s profit. 43. Assume one unit of advertising costs $1. The profit function is The resulting first-order conditions are p (100 Q A 1/2 )Q 10Q A p/a (Q/2)A 1/2 1 0 p/q 100 2Q A 1/2 10 0 A * 900 Q * 60 p * 70 44. Given the demand and cost information, the profit function is The resulting first-order conditions are Solving for A * and Q * yields p (a bq ca a )Q mq A p/a acqa a 1 1 0 p/q a 2bQ ca a m 0 A * (acq * ) (1/a 1) with Q * is solution to (a m) 2bQ c(acq * ) (a/a 1) 0. 45. If pharmaceutical firms are rational, then they advertise because advertising increases their profit. Profit is revenue less total cost. It is reasonable then to infer that as sales increase due to advertising, production and distribution costs of pharmaceutical companies increase slower than revenue. 35

46. Solution provided in Jim Dearden s audio presentation. 47. Solution provided in Jim Dearden s audio presentation. Ch13 1.See Figure 13.1 in the text. Each cartel member has incentive to cheat, reasoning that one country increasing the output will not change the price much. At the same time, since the marginal revenue is above marginal cost, by producing more oil than the agreed upon amount, it can make additional profit. 2. Solution in text. 3. One possibility is that at for places with relatively larger number of firms, the market is segmented. In each market segment, the number of firms is smaller and therefore, they are able to collude and charge a higher price. 4. With only one firm, the deadweight loss is equal to the deadweight loss of a monopoly, that is, (243 147) * (192 96)/2 (243 147) * (243 147)/2 4608 (see Figure 13.2 a in the text). With three firms, the deadweight loss is (195 147) * (195 147)/2 1152, decreasing by 75%. 5. See Figure 13.2. The graph shows response curves for the two airlines. The airline with the lower marginal cost produces more: Southwest transports Q1 passengers and US Air transports Q2 passengers. This result is shown algebraically in Solved Problem 13.1. Figure 13.2 6. The increase in price after the exit of one firm is consistent with a Cournot equilibrium, where the equilibrium price is decreasing in the number of firms. We have to assume that the painkillers are homogeneous for this model to work. 7. The best response function of Firm 2 is a m2 bq1 q2 2b 36

Figure 13.3 shows best response functions for Firm 1 and Firm 2. If marginal costs of the two firms are equal, then Nash-Cournot outputs of the firms are also equal (equilibrium e1 ). Increasing marginal cost of the second firm shifts its best response function inward, which leads to lower output of Firm 2 (equilibrium ). e 2 q 2 a m b a m 2b 2 x e1 m2 m m mx 2 e 2 a m 2b a m 2 b q 1 Figure 13.3 8. Governmental subsidy that reduces fixed cost of each firm in an industry would shift each firm s best response curve rightward, resulting in higher output and lower price in a Cournot monopolistic equilibrium. 9. If there are no fixed costs, MC AC. The two conditions that must hold for a monopolistically competitive equilibrium MC MR, and p AC, cannot hold simultaneously. When MC MR, firms earn positive profits, which violates p AC. The solution is indeterminate. 10. Because firms must bear part of the burden of the tax, profits are reduced. With each firm earning smaller profits, beginning from a point where all firm profits are zero, some firms must exit the industry to restore equilibrium. 11. No. As with the monopolist, there is no unique relationship between price and output. A change in demand may produce a change in price but no change in output, a change in output but not price, or a change in both. 12. In Figure 13.11 in the text, a specific tax increases marginal cost by the amount of the tax. Coke s best response function shifts upward, and Pepsi s best response function shifts to the right. The result is that both firms charge higher prices. 13. If the firms are price setters, then we can assume that they are currently in a Bertrand equilibrium. We can evaluate the increase in cost using a figure similar to Figure 13.11 in the text. The increase in marginal cost of between $70 and $270 per vehicle will shift the best response functions outward on their respective axes. The new equilibrium will result in higher prices, but those price increases will not be on the order of $7000, and will not likely be much different than the increase in marginal cost. 37

14. In the Bertrand equilibrium, the price is equal to the competitive price for homogeneous good when there are at least two firms. Hence increasing the number of firms beyond two will not affect the market price. 15. Solution in text. 16. Solution in text. 17. The best response curve of the praised firm shifts out, while the best response curve of the other firm does not shift. This is the result of an outward shift of the demand curve for the praised firm but not the other. The prices of both firms increase, but the price of the praised firm increases by more. See Figure 13.4 below. Figure 13.4 18. Beginning with Equation 13.4 in the text and substituting the new marginal cost levels, the best response functions and output levels become q U 119.5 1/2 q A q A 69.5 1/2 q U q U 113 q A 13 19. Because the profit-maximizing output level is determined by equating residual marginal revenue to marginal cost, the addition of a fixed cost for both firms does not shift the response functions. However, each response function is truncated at the point where output is too low for the firm to cover variable cost (the shutdown point). Thus as long as profits are greater than FC, the output decisions are unchanged. 20. a. If there is a collusion, Firm 1 should produce all output due to its lower marginal cost. The monopoly price and output levels are determined by MR 120 2Q MC 20 120 2Q 20 Q * 50 p * 70 38